logic and proof day 5. day 5 math review goals/objectives review properties of equality and use them...
DESCRIPTION
Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence. Write two-column, flow chart, and paragraph proofs. Prove geometric theorems.TRANSCRIPT
![Page 1: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/1.jpg)
Logic and Proof
Day 5
![Page 2: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/2.jpg)
Day 5Math Review
![Page 3: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/3.jpg)
Goals/ObjectivesReview properties of equality and use
them to write algebraic proofs.Identify properties of equality and
congruence.Write two-column, flow chart, and
paragraph proofs.Prove geometric theorems.
![Page 4: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/4.jpg)
Vocabularyprooftheoremtwo-column proofflow chart proofparagraph proof
![Page 5: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/5.jpg)
A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.An important part of writing a proof is giving justifications to show that every step is valid.
![Page 6: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/6.jpg)
The Distributive Property states that
a(b + c) = ab + ac.
Remember!
![Page 7: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/7.jpg)
Activity
p. 13 of packet
![Page 8: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/8.jpg)
Numbers are equal (=) and figures are congruent ().
Remember!
![Page 9: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/9.jpg)
When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them.
Hypothesis Conclusion• Definitions• Postulates• Properties• Theorems
![Page 10: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/10.jpg)
A theorem is any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs.
![Page 11: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/11.jpg)
A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of the conjecture. In a two-column proof, you list the steps of the proof in the left column. You write the matching reason for each step in the right column.
![Page 12: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/12.jpg)
![Page 13: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/13.jpg)
•If a diagram for a proof is not provided, draw your own and mark the given information on it. But do not mark the information in the Prove statement on it.
•Before you start writing a proof, you should plan out your logic.
Helpful Hints
![Page 14: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/14.jpg)
A second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof.The justification for each step is written below the box.
A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.
![Page 15: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/15.jpg)
![Page 16: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/16.jpg)
Work Time
•Complete pages 14-16 in your workbook•Completed, correct pages will be stamped •Return to class bin when you are finished
![Page 17: Logic and Proof Day 5. Day 5 Math Review Goals/Objectives Review properties of equality and use them to write algebraic proofs. Identify properties of](https://reader033.vdocuments.mx/reader033/viewer/2022051303/5a4d1b617f8b9ab0599ad778/html5/thumbnails/17.jpg)
Exit QuizComplete the quizShow any and all work that you canCircle your answersTurn in before you leave